证明线性去噪器在图像重建中可保证算法收敛
On the Strong Convexity of PnP Regularization Using Linear Denoisers
- 用线性去噪器构建凸优化问题，确保算法稳定
- 证明该优化问题具有强凸性，收敛性可严格验证
- 适合研究图像重建算法理论的学者参考
在插件式去噪（PnP）方法中，去噪器被用作经典邻近算法中的正则项进行图像重建。已知一类广泛使用的线性去噪器可表示为某个凸正则项的邻近算子，因此相应的PnP算法可关联到一个凸优化问题 𝒫。本文针对此类线性去噪器，证明了在各类线性逆问题下，𝒫 具有强凸性。具体而言，该强凸性可用于验证由经典邻近方法导出的任意PnP算法的目标函数和迭代过程均收敛。
原文摘要 · Abstract (English)
In the Plug-and-Play (PnP) method, a denoiser is used as a regularizer within classical proximal algorithms for image reconstruction. It is known that a broad class of linear denoisers can be expressed as the proximal operator of a convex regularizer. Consequently, the associated PnP algorithm can be linked to a convex optimization problem $\mathcal{P}$. For such a linear denoiser, we prove that $\mathcal{P}$ exhibits strong convexity for linear inverse problems. Specifically, we show that the strong convexity of $\mathcal{P}$ can be used to certify objective and iterative convergence of any PnP algorithm derived from classical proximal methods.
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